翻訳と辞書 Words near each other ・ Primordial black hole ・ Primordial cyst ・ Primordial Divinity (Tai Di) ・ Primitive Calculators ・ Primitive Catholic ・ Primitive cell ・ Primitive Church of Jesus Christ ・ Primitive Church of Jesus Christ (Bickertonite) ・ Primitive communism ・ Primitive Cool ・ Primitive culture ・ Primitive Dance ・ Primitive data type ・ Primitive decorating ・ Primitive element ・ Primitive element (co-algebra) ・ Primitive element (finite field) ・ Primitive element theorem ・ Primitive Enema ・ Primitive equations ・ Primitive Graven Image ・ Primitive groove ・ Primitive Hall ・ Primitive hut ・ Primitive ideal ・ Primitive Instinct ・ Primitive Irish ・ Primitive knot ・ Primitive koa finch ・ Primitive Love Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Primitive element (co-algebra) ： ウィキペディア英語版 Primitive element (co-algebra) In algebra, a primitive element of a co-algebra ''C'' (over an element ''g'') is an element ''x'' that satisfies :$\backslash mu(x)\; =\; x\; \backslash otimes\; g\; +\; g\; \backslash otimes\; x$ where $\backslash mu$ is the co-multiplication and ''g'' is an element of ''C'' that maps to the multiplicative identity 1 of the base field under the co-unit (''g'' is called group-like). ''C'' is said to be primitively generated if it is generated by primitive elements. If ''C'' is a bi-algebra; i.e., a co-algebra that is also an algebra, then one usually takes ''g'' to be 1, the multiplicative identity of ''C''. If ''C'' is a bi-algebra, then the set of primitive elements form a Lie algebra with the usual commutator bracket $(y)\; =\; xy\; -\; yx$ (graded commutator if ''C'' is graded.) If ''A'' is a (certain graded) Hopf algebra over a field of characteristic zero, then the Milnor–Moore theorem states the universal enveloping algebra of the graded Lie algebra of primitive elements of ''A'' is isomorphic to ''A''. == References == *http://www.encyclopediaofmath.org/index.php/Primitive_element_in_a_co-algebra 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Primitive element (co-algebra)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.